Suppose the Laplacians \(L_1\)  and \(L_2\)  correspond to distinct graphs \(G(t)\)  and \(G(t+\Delta t)\)  representing a dynamic multi-agent system at time instants \(t\)  and \((t+ \Delta t)\) , respectively. The above theorem shows the possibility of arising an unusual scenario in a group dynamics, where agent movements do not affect the network connectivity. To this end, in a dense graph with sufficient inter-agent connections, the above phenomenon may exhibit [1]}, where the movement of one agent do not cause any change in the global connectivity. Preserving both the connectivity and the Fiedler vector in distinct graphs can be beneficial in multi-agent dynamics, which is described below using an example.
